While my Year 9 class is starting to move on to Area and Volume, I'm still quizzing them on Expanding and Factorising. At the start of Monday's lesson, I planned to hand out a short set of factorising practice questions to warm up with.

At least, that was the intention. As it turned out, I only remembered that when I walked in the classroom door.

I could've moved straight onto the main activity for that lesson, but I still wanted to do some factorising questions first. So I did what any teacher does when they forget something - pretend that's what the plan was all along. As it turned out, the accidental result was better than my original plan.

I asked students (some volunteers, some I picked on) to give me examples of expressions that can be factorised, which I wrote on the board. I gave everyone a few moments to factorise them, then the class gave me their answers:

(I'm so sorry for my scrawling handwriting. I've never really had the patience to write on the IWB neatly.)

The third one was really interesting. Obviously it can't be factorised, and my reaction at the moment it was suggested was to say that, but fortunately I held my tongue and left it there. That question mark represents a really good discussion the class had about whether this counted as factorising or not. Also, it was awesome that most of the class had already recognised that 1 was the highest common factor of the two terms. They decided it wasn't factorising, because multiplying by 1 doesn't change the expression, and it didn't help simplify the expression.

This is one benefit of getting the class to suggest questions. Had I remembered to organise questions before hand, I would not have used a question like this and not led to that discussion.

I pointed out that all the questions had a numerical common factor. "Is this the only type of factorisation?" I asked. This led to a whole new round of student given questions:

With these, I love how a couple of students recognised that using x2 allowed them to make x the common factor. I also love how the last student refused to allow that pattern to continue, so looked for a different example. There's much deeper thinking going on here - rather than just giving the answers, students were able to think about and discuss the nature of expressions and how they can be factorised. Which is pretty cool for a warm-up activity I didn't plan.

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Shaun used to be maths, IT and ocassional physics teacher at a small P-12 school (primary and secondary) in rural Victoria, Australia. He is currently in the process of starting his career again in the United States.

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